The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
Sensor 
GSD (m) 
Stereo angle 
(degree) 
MOMS-2P 
18 
(2 x) 21.45 
SPOT-5 HRS 
10/5 
40 
ALOS / PRISM 
2.5 
(2 x) 23.8 
CARTOSAT-1 
2.5 
31 
IKONOS-2 
1 
~30 
(Special: 10/6) 
QuickBird 
0.6 
~60 
Table 2: Stereo angles and stereo missions 
2.2 RPC correction 
In (Lehner et al. 2006) it is shown for the stereo pair M1A/F 
that for a full scene a pure bias correction of RPC results in 
residuals which are not acceptable: larger than 1 pixel and with 
systematic behaviour. Since then better GCP could be retrieved 
for all stereo pairs. By their use this finding can be consolidated: 
for full CARTOSAT-1 stereo pairs the correction of the 
provider supplied RPC via an affine transformation is necessary 
to achieve sub-pixel accuracy. Table 3 gives the summary of 
bias versus affine correction for all the stereo pairs used at DLR 
for CSAP. 
Image 
Number 
of 
GCP 
Standard deviation of residuals after 
bias correction 
affine correction 
row 
column 
row 
column 
Cat-A 
70 
0.74 
0.58 
0.51 
0.41 
Cat-F 
68 
1.64 
0.53 
0.56 
0.44 
MIA 
31 
1.39 
3.38 
0.76 
0.56 
M1F 
30 
2.38 
4.46 
0.73 
0.68 
M2A 
9 
1.12 
1.46 
0.43 
0.45 
M2F 
9 
1.59 
1.20 
0.34 
0.33 
Bav- 
AT 
14 
0.48 
0.56 
0.35 
0.53 
Bav-FT 
14 
0.80 
0.64 
0.64 
0.62 
Bav-A 
full 
scene 
30 
1.17 
0.60 
0.50 
0.54 
Table 3: Standard deviations of residuals at GCP after bias and 
affine correction of RPC for various CARTOSAT-1 stereo pairs 
For smaller parts of the images as for the Bavarian Taching test 
area (GCP only in this area indicated by the image names Bav- 
AT/FT - this is about 1/9* of a full scene) a bias correction may 
lead to acceptable results for this sub-area. In order to illustrate 
the nature of the residuals for bias and affine RPC correction 
the shifts are plotted in figures 1 and 2 for the Catalonian case 
with the large number of accurate GCP. It can be seen that the 
pattern of the residuals in the bias case is rather complex and 
can not even be handled by just an additional rotation. In 
contrast, the residuals in figure 2 from the correction with an 
affine transformation do not show any systematic behaviour. Of 
course, if only an inadequate distribution of GCP is available it 
may be worse to do affine instead of bias correction. A well 
distributed set of GCP of high accuracy is needed for an 
optimal result. 
In (Lehner et al. 2007) it has been reported already that forward 
intersection results are often poor without RPC correction (too 
large residuals in image space). 
Figure 1: Residual vectors from bias correction for the 68 GCP 
for Cat-F 
Figure 2: Residual vectors from affine transformation correction 
for the 68 GCP for Cat-F 
2.3 RPC forward intersection 
Forward intersection is done via iterative least squares 
adjustment using 2n (for n stereo partners) observation 
equations (Grodecki et al. 2004, Lehner et al. 2006). Normally, 
in this report on CARTOSAT-1 n is 2 and 4 equations are 
established per stereo tie point for the derivation of the 3 object 
space coordinates longitude, latitude and ellipsoidal height in 
WGS84 datum. The initial values for the object space 
coordinates longitude and latitude are derived from an affine 
transformation using the comer coordinates given by the image 
provider. Initial height values are taken from a DTM (or, 
alternatively, the mean height of the area under investigation 
can be used - this is not critical for the convergence). Normally, 
convergence is achieved after 2 iterations. If a DTM/DSM is 
given as an additional input a statistic of the differences of the 
generated heights and the reference DTM/DSM heights is 
established. 
The residuals in image space can be used for blunder detection. 
Of course, only residuals in cross track direction will be 
effective because wrong row coordinates of tie points are 
translated into wrong height values if only two stereo partners